As of this writing, this feature is not released in stable version of Chrome. It is still being experimented and played with. The version of my Chrome is: 44.0.2403.157 (from chrome://chrome). Then how did I get this feature, you ask? Well, there’s something called Chrome Experimental Labs (chrome://flags), this is the place from where un-released features can be enabled and tested.
Here’s what chrome://flags has to say about itself:
WARNING: These experimental features may change, break, or disappear at any time. We make absolutely no guarantees about what may happen if you turn one of these experiments on, and your browser may even spontaneously combust.
If you want to mute tabs in Google Chrome, you need to enable a/an feature/experiment from chrome://flags. Beware though, because doing so may break or compromise your Chrome. So open a new tab, go to chrome://flags (doesn’t require Internet), press Ctrl (Command for Mac) + F and type “tab audio muting“. Click “Enable” and relaunch Chrome for it to work.
How it works, exactly?
You may know that Chrome shows a little speaker icon on tab playing sound. Once you enable this feature, you can click this icon and mute a particular tab.